Question: Simplify the following expression: $ y = \dfrac{-4}{9} + \dfrac{-9k}{5k + 1} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5k + 1}{5k + 1}$ $ \dfrac{-4}{9} \times \dfrac{5k + 1}{5k + 1} = \dfrac{-20k - 4}{45k + 9} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-9k}{5k + 1} \times \dfrac{9}{9} = \dfrac{-81k}{45k + 9} $ Therefore $ y = \dfrac{-20k - 4}{45k + 9} + \dfrac{-81k}{45k + 9} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{-20k - 4 - 81k}{45k + 9} $ $y = \dfrac{-101k - 4}{45k + 9}$